The human visual system assigns constant
chromatic attributes to objects in spite of the alterations in spectral
distribution of the illuminant or the spatio-chromatic arrangement of the
visual field. This visual capacity is called colour constancy. An example
of this is shown below:

Artificial vision systems that operate
by using the (linear) tristimulus colorimetry do not have this ability,
so they give rise to significant chromatic errors when operating outdoors.
As an example, figure (a) shows the change of the chromatic coordinates
of a set of Munsell samples when changing the illuminant (from CIE C to
CIE A).

According to the retinex theory, in this
work we have implemented different versions of algorithms for colour constancy
[Martínez96, Martínez97].
We proposed new non-linear colour descriptors for a stimulus, practically
invariant to the spectral change of the illuminant. Not
surprisingly, the proposed descriptors are based in normalization of the
tristimulus values by the tristimulus values of the surroundings as in
other color appearance models [Fairchild98]
or in contrast divisive normalization models[Simoncelli01].
Finally, we check experimentally the statistical stability of these descriptors
corresponding to standard colour samples against a range of standard illuminants
as well as their validity rank. Figure (b) shows that the proposed descriptors
are far more stable than chromatic coordinates under a variety of different
illuminants.

(a)

(b)

Colorlab
and the corresponding pair paradigm (see below the application to predict
dichromatic perception) allows the interested reader to play with other
(more standard) color appearance models to obtain color descriptions with
color constancy.

In the literature of color appearance [Fairchild98],
two scenes are referred as to be corresponding scenes if (despite their
physical differences, e.g. different illumination) they give rise to the
same color perception. Invertible color appearance models that incorporate
surround information can be easily used to compute corresponding scenes
by changing the values of the surround under the new illumination conditions. Color appearance models, m, commonly
operate computing the perceptual description of the test, Utest=(Brightness,
Hue, Saturation), from the tristimulus descrption of the test, Ttest
,
and the tristimulus description of the surround, Tsurr
:

Utest = m( Ttest,Tsurr
)

When illumination conditions change, the
tristimulus description of test and surround change, but the perceptual
description, U, does not. This can be used to compute color descriptions
with color constancy or to compute corresponding scenes by using:

Ttest' = m-1(
m(
Ttest , Tsurr ) , Tsurr'
)

In our work on
dichromats perception simulation [Capilla04]
we adapt the above corresponding pair ideas to the case of observers with
different observation conditions: normals and dichromats, but experiencing
the same color perception.The dichromatic color appearance of a
chromatic stimulus T can be described if a stimulus S is
found that verifies that a normal observer experiences the same sensation
viewing
S as a dichromat viewing T. If dichromatic and normal
versions of the same color vision model are available (using the parameters
p and p'), S can be computed by applying the inverse of the normal
model to the descriptors of T obtained with the dichromatic model.
We give analytical form to this algorithm, which we call the corresponding-pair
procedure:

S = m-1( m(
T, p') , p )

The analytical form highlights the requisites
that a color vision model must verify for this procedure to be used. To
show the capabilities of the method, we apply the algorithm to different
color vision models that verify such requisites. This algorithm avoids
the need to introduce empirical information alien to the color model used,
as was the case with previous methods. The relative simplicity of the procedure
and its generality makes the prediction of dichromatic color appearance
an additional test of the validity of color vision models. In the example
below, we show how different dichromats see the Picasso's Dora Maar:

Color
Representation Spaces

In these review works [Capilla98,
Capilla02],
we analyse and compare several linear and non-linear colour representation
spaces at different physiological levels, show the relationships between
spaces and discuss the mathematical properties they should exhibit. At
the photoreceptor level we examine the
cone excitation and cone
contrast spaces. We discuss the second-stage spaces, usually known
as ATD-spaces, paying particular attention to Boynton's space and including
a non-linear space, the opponent modulation space. In addition,
we approach third-stage transformations, which might take place at the
cortical level. Finally, we analyse a perceptual ATD-type space, discussing
how it might be derived as a third-stage transformation of an LGN-based
ATD-space.

CRT
Calibration

In this book chapter [Malo02]
(in spanish!) we analyze the general problem of color reproduction. However,
we restrict ourselves to the solution in CRT monitors. Appropriate references
of the mathematical techniques required to solve the problem are given:
fitting techniques, solution of non-linear equations and multidimensional
interpolation.Here the experimental procedure for standard
(Super VGA) CRT calibration is explained in detail. The results show that
luminance and chromaticity can be accurately reproduced with errors smaller
than 5%. The procedure described here has been incorporated in the Colorlab
Toolbox. The results below show the available colors
in a generic CRT monitor.